Optimal Investment and Equilibrium Pricing under Ambiguity

TL;DR

This paper analyzes portfolio choice and market equilibrium under ambiguity, revealing how ambiguity preferences influence demand, trading, and market phenomena like liquidity and risk premia.

Contribution

It introduces a nonparametric ambiguity model showing strict concavity, nondifferentiable demand functions, and conditions for equilibrium existence and market phenomena.

Findings

Demand functions resemble bid-ask spreads

Heterogeneity in ambiguity preferences enables trade

Equilibria explain liquidity dry-ups and negative risk premia

Abstract

We consider portfolio selection under nonparametric $\alpha$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are nondifferentiable, resemble observed bid-ask spreads, and are consistent with existing parametric limiting participation results under ambiguity. Ambiguity seekers exhibit a discontinuous demand function, implying an empty set of reservation prices. If agents have identical, or sufficiently similar prior beliefs, the first-best equilibrium is no trade. Simple conditions yield the existence of a Pareto-efficient second-best equilibrium, implying that heterogeneity in ambiguity preferences is sufficient for mutually beneficial transactions among all else homogeneous traders. These equilibria reconcile many observed phenomena in liquid high-information financial markets, such as liquidity dry-ups, portfolio inertia, and negative risk premia.